We consider the nonlinear knapsack problem with separable nonconvex functions. Depending on the assumption on the integrality of the variables, this problem can be modeled as a nonlinear programming or as a (mixed) integer nonlinear programming problem. In both cases, this class of problems is very difficult to solve, both from a theoretical and a practical viewpoint. We propose a fast heuristic algorithm, and a local search post-optimization procedure. A series of computational comparisons with a heuristic method for general nonconvex mixed integer nonlinear programming and with global optimization methods shows that the proposed algorithms provide high-quality solutions within very short computing times.

Heuristic algorithms for the general nonlinear separable knapsack problems,

D'AMBROSIO, CLAUDIA;MARTELLO, SILVANO
2011

Abstract

We consider the nonlinear knapsack problem with separable nonconvex functions. Depending on the assumption on the integrality of the variables, this problem can be modeled as a nonlinear programming or as a (mixed) integer nonlinear programming problem. In both cases, this class of problems is very difficult to solve, both from a theoretical and a practical viewpoint. We propose a fast heuristic algorithm, and a local search post-optimization procedure. A series of computational comparisons with a heuristic method for general nonconvex mixed integer nonlinear programming and with global optimization methods shows that the proposed algorithms provide high-quality solutions within very short computing times.
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11585/103861
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